【LeetCode】70 - Climbing Stairs

You are climbing a stair case. It takes n steps to reach to the top.

Each time you can either climb 1 or 2 steps. In how many distinct ways can you climb to the top? 

Hide Tags:   Dynamic Programming

 

Solution:一个台阶的方法次数为1次，两个台阶的方法次数为2个。n个台阶的方法可以理解成上n-2个台阶，然后2步直接上最后一步；或者上n-1个台阶，再单独上一步

 

 1 int climbStairs(int n) {    //Runtime:0ms

 2     int a=1,b=2;

 3     if(n==1)return a;

 4     if(n==2)return b;

 5     int c=0;

 6     for(int i=3;i<=n;i++){

 7         c=a+b;

 8         a=b;

 9         b=c;

10     }

11     return c;

12 }

13 int climbStairs2(int n){    ////Runtime:0ms

14     if(n <= 2)return n;

15     int* step = new int[n];  

16     step[0] = 1;  

17     step[1] = 2;  

18     for(int i = 2; i < n; i++)step[i] = step[i-1] + step[i-2];  

19     return step[n-1];  

20 }